Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x+4y &= 1 \\ -x-y &= 1\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-x = y+1$ Divide both sides by $-1$ to isolate $x$ $x = {-y - 1}$ Substitute this expression for $x$ in the first equation. $3({-y - 1}) + 4y = 1$ $-3y - 3 + 4y = 1$ Simplify by combining terms, then solve for $y$ $1y - 3 = 1$ $1y = 4$ $y = 4$ Substitute $4$ for $y$ in the top equation. $3x+4( 4) = 1$ $3x+16 = 1$ $3x = -15$ $x = -5$ The solution is $\enspace x = -5, \enspace y = 4$.